Auwvax.351
net.misc
utzoo!decvax!harpo!uwvax!doug
Tue May  4 20:15:15 1982
polarizers and the quantum watched pot

			* this is the RIGHT article *

I think the answer to

------->      |/-    (>

is

	If the light is incident on the first filter with an
	intensity of I, then the light which passes through
	the middle filter leaves with an intensity of I * cos^2 (45)
	and the light which leaves the right-most filter has
	an intensity of I * cos^4 (45).

    ------------------------------------------------------------

Anyway, what's *really* interesting here is an extension to this problem.

It reminds me of an article I read a year or so ago in the American Journal 
of Physics.  It purports to relate this sort of classical phenomena 
to the quantum mechanical principle that "the closer you watch a state, 
the less it changes".  As a matter of fact, in the limit where you 
*continously* watch a state, the state never changes.  For example, 
if you could continously watch a certain unstable nuclide it would 
never decay (certainly a change of state).

The description of the classical experiment was this:

	Suppose you had a rectangular tube containing some
	optically active liquid.


		|               |
		|               |
		<------L-------->

	If the tube has length L, and the liquid is optically active,
	then linearly polarized light, say vertical, which passed
	through it would emerge at a polarization of some angle
	theta from the vertical:


	----> | |		|    |   /
		|		|    |
		<------L-------->   (polarizer)

	A vertical polarizer positioned at the right side could be
	used to measure theta by seeing what fraction of the intial
	intensity of light gets through it.

	A SECOND vertical polarizer placed half-way through the tube 
	would mean that a GREATER intensity of light would emerge
	from the far right polarizer than had the second polarizer
	not been there.

	That is, cos^4 (theta/2) is greater than cos^2 (theta).
	(at least for angles of interest in this problem).

	A third polarizer would mean even more got through.  
	And so on, and so on.  Obviously in the
	limit of an infinite number of infinitely thin vertical polarizers
	throughout the whole liquid, the exact same intensity of light
	would emerge finally as intially was incident on the liquid.

The mathematics of closely watched quantum states is very
analagous.  The quantum mechanical state of a system changes
with time, however it changes less when more measurements are made
of it.

The quantum mechanical watched pot never boils.





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